The present invention relates to a method for performing a logarithmic polar coordinate transformation with a high accuracy by using an optical information processing apparatus and a vision recognizing method to be carried out by using the above method.
As a conventional art, Japanese Laid-Open Patent Publication No. 2-57118 has been proposed by the present inventor(s) to perform a logarithmic polar coordinate transformation by using an optical information processing apparatus.
FIG. 9 shows the fundamental construction of the conventional optical information processing apparatus. Reference numeral 1 denotes a television camera (hereinafter referred to as TV camera) capable of varying zoom ratio; 2 denotes a first liquid crystal display for displaying an image picked up by the TV camera 1; 3 denotes a laser diode; 4 denotes a collimator lens which makes beams emitted by the laser diode 3 parallel with each other; 6 denotes a second liquid crystal display adjacent to the first liquid crystal display 2; and 7 denotes a lens. The second liquid crystal display 6 is disposed on the first focal plane of the lens 7. Reference numeral 8 denotes a photoelectric converting device which is disposed on the second focal plane of the lens 7. Reference numeral 309 denotes a read only memory (ROM) onto which data of a computer-generated hologram calculated beforehand with each pixel of the second liquid crystal display 6 being a sampling point is written, i.e., an applied voltage corresponding to the transmission coefficient of each pixel is written to perform a logarithmic polar coordinate transformation of an input image.
The operation of the conventional art optical information processing apparatus constructed as above is described. First, when an object is picked up by the TV camera 1, the image thereof is displayed on the first liquid crystal display 2. The first liquid crystal display 2 is irradiated by coherent beams emitted by the laser diode 3 and made to be parallel with each other by the collimator lens 4. At this time, the phase information of a phase filter for optically transforming the input image in logarithmic polar coordinate is displayed on the second liquid crystal display 6 in the form of a computer-generated hologram by spatially modulating the transmission coefficient of each pixel of the second crystal display 6 with data written onto the ROM 309 being an input signal to the second liquid crystal display 6. For example, the method for generating the phase information of a phase filter is described in "Real-time deformation invariant optical pattern recognition using coordinate transformations" written by David Casasent et al., APPLIED OPTICS, vol. 26, No. 5, March, 1, 1987.
Accordingly, the input image displayed on the first liquid crystal display 2 and the phase information for optically transforming the input image in logarithmic polar coordinate are superimposed on each other on the second liquid crystal display 6. Since the second liquid crystal display 6 is disposed on the first focal plane of the lens 7, the optical product of the input image of the object and the phase information for optically transforming the input image in the logarithmic polar coordinate is optically Fourier-transformed by the lens 7, and an image obtained by transforming the input image of the object in the logarithmic polar coordinate is detected by the photoelectric converting device 8.
FIG. 10(b) shows the result of a computer simulation of a doughnut-shaped input image shown in FIG. 10(a) performed by the optical information processing apparatus having the above-described construction. The size of each dot of FIG. 10(b) shows the intensity of an image obtained by transforming the input image in the logarithmic polar coordinate. The region enclosed by a rectangle indicates a strict solution.
In recognizing an object which flows on a production line of, for example, a factory, the object can be accurately recognized by performing a pattern matching of the object image and a reference pattern by additionally using an optical correlator in carrying out a logarithmic polar coordinate transformation method which uses the above-described conventional optical information processing apparatus. This is because the value of the object image relative to that of the reference pattern does not change even though the object makes a scale change or rotates.
As described above, a logarithmic polar coordinate transformation has invariability for the scale change or the rotational movement of the object, but does not have invariability for the parallel movement thereof. Therefore, the object cannot be accurately recognized when the object makes a parallel movement. Regarding this disadvantage, it is known that the value of the object image relative to that of the reference pattern is not changed by performing a pattern matching by Fourier-transforming an input image and then transforming the Fourier-transformed input image in logarithmic polar coordinate even though the object makes a scale change, a rotational movement or a parallel movement. Thus, the object can be accurately recognized.
However, according to the construction as described above, the intensity of the coordinate-transformed image becomes lower as approaching the origin of logarithmic polar coordinate and higher in being far from the origin thereof as shown in FIG. 10(b). That is, an intensity gradient is generated in the coordinate-transformed image in the radial direction thereof and therefore, the coordinate transformation cannot be made accurately.
In addition, when the above construction is used as the pre-processing of the pattern matching of the object image, a vision cannot be recognized accurately because the coordinate transformation cannot be made accurately.